Of the students in Emmet's class, 4/5 have a pet cat. Of the students who have a cat, 1/3 also have a dog. What fraction of the students in Emmet's class have both a cat and a dog?


To find the fraction of students in Emmet's class who have both a cat and a dog, follow these steps:

1. **Fraction of students with a cat**:  
   The problem states that \(\frac{4}{5}\) of the students have a cat.

2. **Fraction of students with both a cat and a dog**:  
   Of the students who have a cat, \(\frac{1}{3}\) also have a dog. So, the fraction of the total students who have both a cat and a dog is:
   \[
   \text{Fraction with both} = \frac{4}{5} \times \frac{1}{3}
   \]

3. **Multiplication**:  
   Multiply the fractions:
   \[
   \frac{4}{5} \times \frac{1}{3} = \frac{4 \times 1}{5 \times 3} = \frac{4}{15}
   \]

So, \(\frac{4}{15}\) of the students in Emmet's class have both a cat and a dog.

Would you like more details or have any questions about the solution?

Here are 5 related questions:

1. If there are 30 students in Emmet's class, how many have both a cat and a dog?
2. What fraction of the students in Emmet's class do not have a cat?
3. If \(\frac{2}{3}\) of the students with a dog also have a bird, what fraction of the total class has a cat, dog, and bird?
4. How would the fraction change if \(\frac{2}{5}\) of the students with a cat also had a dog instead of \(\frac{1}{3}\)?
5. If \(\frac{3}{4}\) of the students with both a cat and a dog also have a fish, what fraction of the total class has a cat, dog, and fish?

**Tip:** When multiplying fractions, simply multiply the numerators together and the denominators together.

Explore how to find the fraction of students in Emmet's class who have both a cat and a dog with a step-by-step solution. This problem involves fractions and their multiplication, illustrating basic mathematical concepts suitable for Grades 4-6.

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